4u^2-12u-11=0

Solution for 4u^2-12u-11=0 equation:

Simplifying
4u2 + -12u + -11 = 0

Reorder the terms:
-11 + -12u + 4u2 = 0

Solving
-11 + -12u + 4u2 = 0

Solving for variable 'u'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-2.75 + -3u + u2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + -3u + 2.75 + u2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + -3u + u2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + -3u + u2 = 0 + 2.75
-3u + u2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
-3u + u2 = 2.75

The u term is -3u.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3u + 2.25 + u2 = 2.75 + 2.25

Reorder the terms:
2.25 + -3u + u2 = 2.75 + 2.25

Combine like terms: 2.75 + 2.25 = 5
2.25 + -3u + u2 = 5

Factor a perfect square on the left side:
(u + -1.5)(u + -1.5) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(u + -1.5) equal to 2.236067978 and -2.236067978.

Subproblem 1
u + -1.5 = 2.236067978

Simplifying
u + -1.5 = 2.236067978

Reorder the terms:
-1.5 + u = 2.236067978

Solving
-1.5 + u = 2.236067978

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + u = 2.236067978 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + u = 2.236067978 + 1.5
u = 2.236067978 + 1.5

Combine like terms: 2.236067978 + 1.5 = 3.736067978
u = 3.736067978

Simplifying
u = 3.736067978

Subproblem 2
u + -1.5 = -2.236067978

Simplifying
u + -1.5 = -2.236067978

Reorder the terms:
-1.5 + u = -2.236067978

Solving
-1.5 + u = -2.236067978

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + u = -2.236067978 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + u = -2.236067978 + 1.5
u = -2.236067978 + 1.5

Combine like terms: -2.236067978 + 1.5 = -0.736067978
u = -0.736067978

Simplifying
u = -0.736067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {3.736067978, -0.736067978}